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The arithmetic and geometry of Salem numbers


Authors: Eknath Ghate and Eriko Hironaka
Journal: Bull. Amer. Math. Soc. 38 (2001), 293-314
MSC (2000): Primary 11R06, 11R52, 20F55
DOI: https://doi.org/10.1090/S0273-0979-01-00902-8
Published electronically: March 27, 2001
MathSciNet review: 1824892
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Abstract:

A Salem number is a real algebraic integer, greater than $1$, with the property that all of its conjugates lie on or within the unit circle, and at least one conjugate lies on the unit circle. In this paper we survey some of the recent appearances of Salem numbers in parts of geometry and arithmetic, and discuss the possible implications for the `minimization problem'. This is an old question in number theory which asks whether the set of Salem numbers is bounded away from $1$.


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Additional Information

Eknath Ghate
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400 005, India
Email: eghate@math.tifr.res.in

Eriko Hironaka
Affiliation: Department of Mathematics, Florida State University, Tallahassee, FL 32306
Email: hironaka@math.fsu.edu

DOI: https://doi.org/10.1090/S0273-0979-01-00902-8
Received by editor(s): November 20, 1999
Published electronically: March 27, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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